Subgroups — C₇×C₃⋊(C₃⋊#10597010) #49176389

Order 37548.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×D₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₇×C₃⋊#10597010	—	3	4	no	maximal
3	C₃²×C₇×C₁₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×D₁₄₉	D₃	1	4	yes	—
5	C₃⋊(C₃⋊#10597010)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×#10597010	—	9	1	no	Hall
7	C₃×C₇×C₁₄₉	Dic₃	1	4	yes	complemented
8	C₃²×D₁₄₉	C₂×C₇	1	1	yes	characteristic
9	C₇×D₁₄₉	C₃⋊D₃	1	1	yes	characteristic
10	C₃⋊#10597010	—	3	4	no	—
11	C₃²×C₁₄₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₄₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
13	C₃×D₁₄₉	D₃×C₇	1	4	yes	—
14	#10597010	—	9	1	no	Hall
15	C₃×C₁₄₉	C₇×Dic₃	1	4	yes	complemented
16	D₁₄₉	C₇×C₃⋊D₃	1	1	yes	characteristic
17	C₇×C₃⋊Dic₃	—	149	1	no	maximal, Hall
18	C₁₄₉	C₇×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃²×C₇	—	149	1	no	—
20	C₇×Dic₃	—	447	4	no	—
21	C₃²×C₇	#10597010	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	—	149	4	no	—
23	C₃⋊Dic₃	—	149	1	no	Hall
24	C₄×C₇	—	1341	1	no	Hall
25	C₃×C₇	C₃⋊#10597010	1	4	yes	complemented
26	C₂×C₃²	—	149	1	no	—
27	C₂×C₇	—	149	1	no	—
28	Dic₃	—	447	4	no	—
29	C₃²	C₇×#10597010	1	1	yes	characteristic, complemented, Sylow
30	C₇	C₃⋊(C₃⋊#10597010)	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	149	4	no	—
32	C₄	—	1341	1	no	Sylow
33	C₃	C₇×C₃⋊#10597010	1	4	yes	complemented
34	C₂	—	149	1	no	—

	subgroup	G/H
center, hypercenter	C₇	C₃⋊(C₃⋊#10597010)
commutator, hypocenter	C₃²×C₁₄₉	C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₄₉	C₄
prime radical	C₃²×C₇×D₁₄₉	C₂
cosocle	C₃²×D₁₄₉	C₂×C₇
LCS	G ▷ C₃²×C₁₄₉
UCS	C₁ ◁ C₇

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₃²×C₇×C₁₄₉	C₄	semidirect
5. C₃⋊(C₃⋊#10597010)	C₇	direct (N × H)
7. C₃×C₇×C₁₄₉	Dic₃	semidirect
11. C₃²×C₁₄₉	C₄×C₇	semidirect
12. C₇×C₁₄₉	C₃⋊Dic₃	semidirect
15. C₃×C₁₄₉	C₇×Dic₃	semidirect
18. C₁₄₉	C₇×C₃⋊Dic₃	semidirect
21. C₃²×C₇	#10597010	semidirect
25. C₃×C₇	C₃⋊#10597010	semidirect
29. C₃²	C₇×#10597010	semidirect
30. C₇	C₃⋊(C₃⋊#10597010)	direct (N × H)
33. C₃	C₇×C₃⋊#10597010	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₇×D₁₄₉	2
C₇×C₃⋊#10597010	3
C₃⋊(C₃⋊#10597010)	7
C₇×C₃⋊Dic₃	149

Subgroups — C7×C3⋊(C3⋊#10597010) #49176389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃⋊(C₃⋊#10597010) #49176389